Chapter 6 exercises: probability analysis and calculations môn Xác suất thống kê| Trường Đại học Ngoại Thương

CHAPTER EXERCISES
6.107 Pew Research Center conducted a survey of countries
then the probability of winning contract B decreases
around the world and asked respondents whether
to .2. Find the probability of the fol owing events.
they were having a typical day, a good day, or a bad a. Winning both contracts
day. The results and the number of respondents in Country N Reu s m p b o e n r d o e f n ts Typ D ical ay (% ) G D oo ay ( d %) Bad Day
b. Winning exactly one contract
Europe, Asia, and the United States are listed next.
c. Winning at least one contract
6.110 Laser surgery to fix shortsightedness is becoming
more popular. However, for some people, a second (%)
procedure is necessary. The following table lists the Asia 525 68 30 2
joint probabilities of needing a second procedure Europe 650 76 17 7
and whether the patient has a corrective lens with a
factor (diopter) of minus 8 or less. United 390 49 41 10 States Vision Vision
One respondent is selected at random. Corrective Corrective
Factor of More Factor of Minus
a. Find the probability that the respondent is hav- Factor Than Minus 8 8 or Less ing a good day.
b. The respondent is having a typical day. What is First procedure
the probability that he is from the United States. is successful .66 .15 Second procedure
6.108 The following table lists the joint probabilities of
achieving grades of A and not achieving A’s in two is required .05 .14 MBA courses.
a. Find the probability that a second procedure is required. Does Not
b. Determine the probability that someone whose Achieve a Achieve a Grade of A Grade of A
corrective lens factor is minus 8 or less does
in Marketing in Marketing
notrequire a second procedure.
c. Are the events independent? Explain your answer. Achieve a grade of A
6.111 The effect of an antidepressant drug varies from in statistics .053 .130
person to person. Suppose that the drug is effective Does not achieve a
on 80% of women and 65% of men. It is known that grade of A in statistics .237 .580
66% of the people who take the drug are women.
a. What is the probability that a student achieves a
What is the probability that the drug is effective? grade of A in marketing?
6.112 Refer to Exercise 6.111. Suppose that you are told
b. What is the probability that a student achieves
that the drug is effective. What is the probability
a grade of A in marketing, given that he or she that the drug taker is a man?
does not achieve a grade of A in statistics?
6.113 In a four-cylinder engine there are four spark plugs.
c. Are achieving grades of A in marketing and
If any one of them malfunctions, the car will idle
statistics independent events? Explain.
roughly and power will be lost. Suppose that for a
6.109 A construction company has bid on two contracts.
certain brand of spark plugs the probability that a
The probability of winning contract A is .3. If the
spark plug will function properly after 5,000 miles is
company wins contract A, then the probability of win-
.90. Assuming that the spark plugs operate indepen-
ning contract B is .4. If the company loses contract A,
dently, what is the probability that the car will idle roughly after 5,000 miles?
6.114 A telemarketer sel s magazine subscriptions over the Rating Women Men
telephone. The probability of a busy signal or no Excellent .27 .22
answer is 65%. If the telemarketer does make contact,
the probability of 0, 1, 2, or 3 magazine subscriptions Good .14 .10 is .5, Average .06 .12
.25, .20, and .05, respectively. Find the probabil-
ity that in one call she sel s no magazines. Poor .03 .06
6.115 A statistics professor believes that there is a relation-
a. What proportion of customers rate Casino
ship between the number of missed classes and the Windsor as excellent?
grade on his midterm test. After examining his records,
b. Determine the probability that a male customer
he produced the following table of joint probabilities.
rates Casino Windsor as excellent.
c. Find the probability that a customer who rates Stud t e h nt T F e ai st ls Student Passes
Casino Windsor as excellent is a man. the Test
d. Are gender and rating independent? Explain Student misses fewer your answer. than 5 classes .02 .86
6.118 A customer-service supervisor regularly conducts a Student misses 5 or
survey of customer satisfaction. The results of the more classes .09 .03
latest survey indicate that 8% of customers were
not satisfied with the service they received at their
a. What is the pass rate on the midterm test?
last visit to the store. Of those who are not satisfied,
b. What proportion of students who miss five or
only 22% return to the store within a year. Of those
more classes passes the midterm test?
who are satisfied, 64% return within a year. A cus-
c. What proportion of students who miss fewer
tomer has just entered the store. In response to your
than five classes passes the midterm test?
question, he informs you that it is less than 1 year d. Are the events independent?
since his last visit to the store. What is the probabil-
ity that he was satisfied with the service he received?
6.116 In Canada, criminals are entitled to parole after
serving only one-third of their sentence. Virtually
6.119 How does level of affluence affect health care? To
all prisoners, with several exceptions including mur-
address one dimension of the problem, a group of
derers, are released after serving two-thirds of their
heart attack victims was selected. Each was catego-
sentence. The government has proposed a new law
rized as a low-, medium-, or high-income earner.
that would create a special category of inmates based
Each was also categorized as having survived or died.
on whether they had committed crimes involving
A demographer notes that in our society 21% fall
violence or drugs. Such criminals would be subject
into the low-income group, 49% are in the medium-
to additional detention if the Correction Services
income group, and 30% are in the high-income
judges them highly likely to reoffend. Currently,
group. Furthermore, an analysis of heart attack vic-
27% of prisoners who are released commit another
tims reveals that 12% of low-income people, 9% of
crime within 2 years of release. Among those who
medium-income people, and 7% of high-income
have reoffended, 41% would have been detained
people die of heart attacks. Find the probability that a
under the new law, whereas 31% of those who have
survivor of a heart attack is in the low-income group.
not reoffended would have been detained.
a. What is the probability that a prisoner who
would have been detained under the new law
does commit another crime within 2 years?
b. What is the probability that a prisoner who
would not have been detained under the new
law does commit another crime within 2 years?
6.117 Casino Windsor conducts surveys to determine the
opinions of its customers. Among other questions,
respondents are asked to give their opinion about
“Your overall impression of Casino Windsor.” The responses are Excellent Good Average Poor
In addition, the gender of the respondent is noted.
After analyzing the results, the following table of
joint probabilities was produced.